ES100 TwoDimensional Equilibrium 
SF_{x} = 0 SF_{y} = 0 SM = 0 
For an object to be in equilibrium in twospace three scalar equations of static equilibrium must be satisfied... 
SF_{x} or SF_{y} = 0 SM_{A} = 0 SM_{B} = 0 
Since any three independent equations of equilibrium may be used, an alternate would be the set of equations shown where A and B are two points on the body. 
SM_{A} = 0 SM_{B} = 0 SM_{C} = 0 
Or alternately, three moment equations may be used. Note: Any three nonredundant equations may be used.
Note: Sometimes one equation is trivially satisfied. 
A mass of 10kg is hung from two ropes, AB and BC. Find the tension in each rope.  A statics problem is usually stated with a description, and,
if necessary, a diagram. Lets examine an example... 
The associated space diagram is shown here. 
The space diagram is converted to a free body diagram. For a free body diagram a point or body is isolated and all forces on it are indicated. 

The force equilibrium equations in the x and y directions may then be written... 
F_{BC} = 1.2 F_{AB} from (1) F_{AB} (.707) + F_{AB}(.500) = 98 from (2) F_{AB} = 72.7 N F_{BC} = 87.2 N 
Solving for F_{AB} and F_{BC}... Note: In this case the sum of the moments equation is automatically satisfied since all forces pass through one point. 